It really isn’t.
That’s because you haven’t tried. I can easily bind 40+ keys on a controller, and I’m not using that many bindings on any role to begin with. You’re not limited to 4 buttons + shoulder + triggers. You can do 4 buttons modified by a shoulder button, as if it were a “Shift” or similar.
You can also use oPie for quick access to less used stuff, like invis pots, engi belt, world or mob markers, that kind of stuff. As it happens, oPie is more comfortable to use with a controller than with kb+mouse. 
It works fine in dungeons, even higher keys. I can do the same difficulty keys with a controller as with keyboard + mouse, in any role, without anyone noticing any difference.
I timed +20s in BfA S4 with a controller, as a healer. I tanked and healed KSM in SL S1, healed up to 19s with one. I’ve raided with a controller. It really isn’t a limiting factor, and in many cases, works much better than a keyboard, even.
Why does it work better than keyboard + mouse? Because you don’t have to move your hands at all. You just sit comfortably in your chair, or on the sofa, with the controller in hand, and blast. It’s not slower than a keyboard, it can support way more bindings than you possibly need for WoW, and it’s super comfy.
The only downside is that you need to get used to it, and aiming is a little different. That’s all. Once learned and gotten used to it, noone will ever know you’re playing with a controller. Unless you have to type in chat, that’s something kb+mouse is better at, but hey, we have voice comms.
I’m currently healing +16/+17s with one, and tanking the same key levels with a controller, when I feel like it. Noone can tell when I’m playing with controller, and when I am with kb + mouse. There’s literally no difference in performance.